source file: mills2.txt Date: Wed, 5 Feb 1997 17:20:43 -0800 Subject: Re: 88CET Definition From: Matt Nathan Gary Morrison wrote: > > > That puts the P5 at > > > about 695.5 cents, which means that it's somewhat similar with 88TET > > > (not > > > to be confused with 88CET). > > > > 88TET stands for 88-tone equal temperament, but what does 8CET stand for? > > 88CET stands for "88-Cent [per step] Equal Temperament". 88TET and > 88CET could be characterized as inverses of each other: 88TET has a step > size of ~13.63c and 88 steps/octave, whereas 88CET has a step size of 88c > and ~13.63 steps/octave. > > This "CET" terminology is my idea, as far as I know. It's convenient > for a naming an equal-temperament whose step-size is an even number of > cents but doesn't work out to any exact subdivision of any particular > integer or integer ratio. 88CET is pretty close to 3 equal steps per 7:6, > 4 per 11:9, 5 per 9:7, 7 per 10:7, 8 per 3:2, 10 per 5:3, 11 per 7:4, 16 > per 9:4, or 18 per 5:2, but it isn't exactly any of those. > > Carlos' alpha could be described as 78CET, and beta as 64CET. Ah, of course. Funny I didn't recognize the C as cents, since I've used a similar notation for the command line interpretation syntax of my MIDI tuning dump equal temperament generator in C (computer language). Here are some examples of the argument syntaxes it understands: ET [generates an equal temperament of random step width] ET 12 [generates 12 tones per octave equal temperament] ET 100 C [generates equal temperament with step size of 100 cents] ET C 100 [same as above] ET 85.33333 Y [generates equal temperament with step size of 85.33333 yamaha tuning units (1024 per octave)] ET Y 85.33333 [same as above] ET 12 2 1 [generates equal temperament of 12 steps per 2/1 ratio] If you allow Y into the terminological extensions, one might write 4TET 300CET 256YET. I also like sometimes to measure intervals in fractions of an octave, such as 3/2 ~0.58496 octaves. This helps detwelvulate (thanks Ivor) the sense that you get from measuring intervals in cents. BTW, it was playing with the random tunings from which I learned the most and that helped me understand that, to my intuitive ear anyway, all ET's lean towards one of two groups, those that provide close approximations of some number of just intervals, and ones that deftly avoid just intervals. There are some raucous ET's which give you almost no pitch combinations which are comfortable at all. Matt Nathan Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 6 Feb 1997 11:06 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA27721; Thu, 6 Feb 1997 11:06:32 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA27825 Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) id CAA10156; Thu, 6 Feb 1997 02:04:06 -0800 Date: Thu, 6 Feb 1997 02:04:06 -0800 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@ella.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@ella.mills.edu